Koolen–Bang classification conjecture for geometric distance-regular graphs

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Let m≥2m \geq 2 be a fixed integer. A geometric distance-regular graph has diameter D≥3D \geq 3 and intersection number c2≥2c_2 \geq 2. Koolen–Bang's classification conjecture. Any geometric distance-regular graph with smallest eigenvalue −m-m is either a Johnson graph, a Grassmann graph, a Hamming graph, a bilinear forms graph, or has number of vertices bounded above by a function of mm. The source presents this as one of two conjectures proposed by Koolen and Bang; no resolution is given, so it remains open.

References

Primary source

Chenhui Lv and Jack H. Koolen, “On the characterization of geometric distance-regular graphs”, arXiv:2601.10330 (2026).

Additional references

2 papers in this index state this conjecture (2020–2026). The statement above is taken from the most recent of them; the others are arXiv:2011.11935.

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